Understanding Uniform Distribution (and Cracking the Data Science Interview)

Understanding Uniform Distribution (and Cracking the Data Science Interview)

In this short post, we are going to solve a few problems involving Uniform Distribution. Uniform Distribution is yet another favorite of many interviewers, and nailing any problems involving Uniform Distribution really makes your candidacy stand out

We are continuing our series on cracking Data Science interviews. So far, we have worked out a [few_](https://medium.com/swlh/linear-regression-and-maximum-likelihood-1dcb9435c71e)[_examples_](https://medium.com/swlh/maximum-likelihood-and-data-science-interviews-c31b1d5b4e4a) on Maximum Likelihood Estimator (MLE). In this short post, we are going to solve a few problems involving Uniform Distribution. Uniform Distribution is yet another favorite of many interviewers, and nailing any problems involving Uniform _Distribution really makes your candidacy stand out 🙂

First and Foremost, the Definition…

A uniform distribution over the bounds a and b has the following probability density function:

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Probability Density Function of Uniform Distribution

Here is the curve for the pdf from Wikipedia:

Recall that the_ Cumulative Distribution Function (CDF) _of a uniform distribution is given by

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Cumulative Distribution Function of Uniform Distribution

We are going to use the CDF (instead of PDF) a lot in this post! Make sure you understand the formula above.

Finally, we are mainly going to deal with a Uniform Distribution over the interval [0, 1]. We are also going to ignore the range outside the interval [0, 1]. The formulae for PDF and CDF simplify to the following forms for this simple interval:

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